AP Calculus Blog

Time to learn about some applications of integrals in the context of the volumes of curves.

This week we talked about how to find the volume that a curve has with respect to either the Y-axis or the X-axis, which depends on how the equations are set up or how the curves themselves are oriented. We also took a quiz on how to use the integral in order to find the area in between two curves on Wednesday. I thought the quiz wasn't THAT hard. But I did realize that I messed up on two of the problems right after I turned it in. Like literally, right as I set the freaking paper down on my teacher's desk I realized that I f-d up on a problem. Which is always a great sign right?

Talking about the volume under a curve stuff. We can use the integral of a function in order to find the volume of the curve when it is spun around either the x or y axes. What you have to do is just basically use the integral notation, put in the bounds of the function, plug in the area function of the solid that is formed once the curve is spun around the axes, then just used NINT on your calculator. Or you can do it manually, but who wants to do that?